I haven't had a need to tighten the awning, but have changed one out. The awning is shipped with a big clevis pin going through one side of the round housing, the shaft of the rotating part, and out the housing on the other side. If you look at the housing just inboard of short locking arm, you should see a hole in the housing and another one on the other side. If the shaft happens to be in just the right position, you can see all the way through.
Some one will probably come up with an easier way of doing this, but this procedure should prevent busted knuckles...
1) Run the slideout all the way out.
2) Manually unroll the awning slightly further, if necessary, to line up the holes in the housing and shaft. You can use a big screwdriver in the slot of the housing, if needed.
3) Insert large clevis pin or substitute.
4) Dismount the awning brackets from the slideout. (Never, ever do this without the clevis pin inserted)
5) Manually roll up the awning one turn. (Just rotate the whole housing, shaft, bracket assembly around the loose awning material)
6) Run the slideout all the way back in and then run it partially back out till it matches up with the awning.
7) Remount the awning brackets to the slideout.
8) Remove the clevis pin.
9) Run the slideout on out till fully open.
That should add one turn of tension to the awning. If you feel that won't be enough, modify step 5.
Good luck and be very careful. If that tension gets loose, it can do a lot of damage to you and the RV - just keep it under control with the clevis through the shaft...
On edit: After reading the thread supplied by Jim, change all my references to a clevis pin to read cotter pin. Don't know where I got clevis...
From reading the other posts, adding tension doesn't sound like a great idea anyway.